Monocrystalline solid state materials, such as single-crystal semiconductors, are the basis of the current microelectronics industry. Each single crystalline solid is a periodic structure in space, with a basic repeating unit called the unit cell. Crystalline solids are characterized by a variety of properties, for example, electrical properties such as electrical conductivity or charge mobility, optical properties such as refractive index or speed of photons, thermal properties such as thermal conductivity or thermal expansion, mechanical properties such as stress or strain curves, and chemical properties such as resistance to corrosion or reaction consistency, among others.
Over the past ten years, theoretical end experimental interests have evolved around the electromagnetic radiation propagating in periodic crystalline structures. The core of these experiments has been the condition for the elastic diffraction of X rays (electromagnetic waves) in a crystal, a phenomenon in which the X rays change their direction without changing their frequencies, and consequently, without changing their energies. The condition that an incident beam of X rays q0 comes off in the same direction from each scattering center is exemplified in FIG. 1. On a line of atoms of the same kind, situated along the x-axis of a crystal and spaced apart at a distance “a” (in a normal crystal, atoms are spaced apart at a distance “a” of about 4-5 Angstroms), an X ray beam q0 with a definite wave vector impinges on the line of atoms from an angle α0 and comes off with wave vector q in the direction α, as shown in FIG. 1. The condition that the beam q0 comes off in the same direction from each scattering center is the following formula:a(cos α−cos α0)=Nλ  (1)
wherein: a=the distance between any two adjacent atoms or scattering centers;                                    α0=the incidence angle of the X ray beam;            α=the diffraction angle of the X ray beam;            N=an integer; and            λ=the wavelength of the X ray beam.                        
The equation (1) is the condition that the scattered waves interfere constructively in the direction q, so that the beam of X rays sent into a crystal comes out scattered coherently, elastically, into various directions, each of which representing a momentum transfer that satisfies equation (1). As known in the art, equation (1) applies to other scattering/diffraction structures such as gamma rays, electron beam, ions, and photons, among others.
It is well-known that electrons in ordinary matter exhibit behavior analogous to the diffraction of light waves in crystalline solids which was exemplified above and quantified by equation (1). As such, it is now common knowledge that electrons in a crystalline solid produce electrical conductivity by a constructive interference of various scattering trajectories, as a result of the diffraction of electrons from the periodic potential of the atomic lattice. This way, the wave nature of the electrons and the periodic lattice of atoms can give rise to both allowed energy bands (a result of the constructive interference effects of electrons) and forbidden energy gaps, also called electron bandgaps (a result of the destructive interference effects of electrons) for the electrons in a crystalline solid. These constructive and destructive interferences of electrons in superlattices are the basis of the electronic behavior of metals, semiconductors and insulators, which are of fundamental importance to the semiconductor industry.
Over the past years, the creation of analogous forbidden electromagnetic or photonic bandgaps in crystalline solids has been recognized as a promising way of obtaining novel properties in crystalline solids. Similar to the case of electrons, the photonic bandgaps arise from the destructive interference effects of electromagnetic waves for certain wavelengths and directions, and are characterized by the inhibition of optical propagation in the crystal. An experiment by Yablonovitch et. al (E. Yablonovitch. Phys. Rev. Lett., 58, 2059 (1987)) has suggested that the electromagnetic radiation propagating in periodic dielectric structures is similar to the electron waves propagating in a crystal. Yablonovitch et. al realized that setting up a periodic index of refraction pattern in a material can produce a band structure for electromagnetic waves where certain wavelengths can or cannot propagate, producing therefore the electromagnetic wave equivalent of a metal, semiconductor or insulator. If the wavelength is in the order of the dimensions of the crystal lattice, a photonic bandgap (a frequency range where photons are not allowed to propagate) can open up in two or three dimensions and lead to interesting phenomena, such as inhibition of spontaneous emission from an atom that radiates inside the photonic gap or frequency selective transmission and reflection. This way, for example, if a photonic crystal can be constructed to possess a full photonic bandgap, then a photonic insulator is created by artificially controlling the optical properties of the solid.
Since the findings of Yablonovitch et al, numerous experiments have been carried out to realize photonic bandgap effects at optical wavelengths. For example, in Direct visualization of photonic band structure for three-dimensional photonic crystals, Phys. Rev. B, 61, 7165 (2000), Notomi et al. have realized photonic bandgap effects by using shape formation by bias sputtering. For this, the experiments and measurements of Notomi et al. were carried out on a three-dimensional periodic index of refraction structure, that is a Si/SiO2 alternating-layer 3D hexagonal photonic crystal fabricated by autocloning bias-sputtering deposition, and illustrated in FIG. 2.
Similarly, Gruning et al. have fabricated a two-dimensional photonic band structure in macroporous silicon, with pores grown in a random pattern and formed by an electrochemical pore formation process (Two-dimensional infrared photonic bandgap structure based on porous silicon, Appl. Phys. Lett. 68, 747 (1996)). Zakhidov et al. also realized a three-dimensional porous carbon formed by sintering crystals of silica opal to obtain an intersphere interface through which the silica was subsequently removed after infiltration with carbon or a carbon precursor (Carbon Structures with Three-Dimensional Periodicity at Optical Wavelengths, Science, 282, 897 (1998)).
One of the limitations inherent in all the above-mentioned photonic lattices experiments is the requirement that the dimensions of the lattice must be in the same order of magnitude as the desired band gap wavelength, or in other words, the refractive index variations or discontinuities should have periodicities on the same scale as the wavelength. As the dimensions of the lattice must be in the same order of magnitude as the desired band gap wavelength, the scaling down to the interesting optical and infrared frequencies has posed problems due to the demanded regularity and uniformity of the photonic lattice. In addition, as two-dimensional photonic band gaps structures are technologically easier to fabricate, recent fabrication methods have focussed mainly on two dimensions, particularly on a regular hole structure in a dielectric material, and not on the more complex three dimensions. Further, although sub-micron photonic structures have been successfully fabricated in AlGaAs and/or Gas, extreme process conditions are necessary to achieve lattice depths of less than a micron in these structures.
Accordingly, there is a need for an improved method of fabricating three-dimensional photonic bandgap structures in a wide variety of solid materials, such as monocrystalline substrates, dielectrics, superconducting materials or magnetic materials, among others. There is also a need for a more advantageous method of generating a wide variety of space group symmetries, with different group symmetries for wavelength regions of interests, in such variety of solid materials. A method of controlling the dimensions of photonic lattices to acquire a predetermined band structure for electromagnetic waves so that diffraction occurs in a specific, predetermined wavelength is also desired.